Given the context of Isaiah, I always seen the expression כל בשר as a reference to am yisroel, given the expressions of לא רחמה and לא עמי in Hosea 1-2. I've always understood it as all Israel in its entirety would end up praising Hashem in unison, והיה מדי חדש בחדשו ומדי שבת בשבתו יבוא כל בשר להשתחות לפני, meaning "all flesh [of Israel] shall end up worshipping Me [alone]". Am I wrong?
Radak and Metzudas David (ad loc.) interpret "כל בשר" as including non-Jews too.
However this is does not indicate that they will keep Shabbos, or that they may keep Shabbos. It merely indicates that they will also come to the Temple to bow before Hashem.
The Jews will walk, and the non-Jews can drive!